Random Jason Timeout Test 003

Average Error: 0.1 → 0.1

Time: 26.5s

Precision: 64

• could not determine a ground truth for program body

  1. a = 8.504910344707986e+189
  2. b = 1.9244747225358218e-24

Math

\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]

↓

\[\sin \left(e^{\frac{\left(\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)} \cdot \sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}\right) \cdot \sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}}{\frac{4}{b - a}}} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]

C

double f(double a, double b) {
        double r1128198 = b;
        double r1128199 = atan2(r1128198, r1128198);
        double r1128200 = sqrt(r1128199);
        double r1128201 = a;
        double r1128202 = r1128198 - r1128201;
        double r1128203 = pow(r1128200, r1128202);
        double r1128204 = sin(r1128203);
        return r1128204;
}

↓

double f(double a, double b) {
        double r1128205 = b;
        double r1128206 = atan2(r1128205, r1128205);
        double r1128207 = log(r1128206);
        double r1128208 = cbrt(r1128207);
        double r1128209 = r1128208 * r1128208;
        double r1128210 = r1128209 * r1128208;
        double r1128211 = 4.0;
        double r1128212 = a;
        double r1128213 = r1128205 - r1128212;
        double r1128214 = r1128211 / r1128213;
        double r1128215 = r1128210 / r1128214;
        double r1128216 = exp(r1128215);
        double r1128217 = sqrt(r1128206);
        double r1128218 = sqrt(r1128217);
        double r1128219 = pow(r1128218, r1128213);
        double r1128220 = r1128216 * r1128219;
        double r1128221 = sin(r1128220);
        return r1128221;
}

Error

Bits error versus a

Bits error versus b

Derivation

1. Initial program 0.1

   \[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
2. Using strategy rm

3. Applied add-sqr-sqrt 0.1

   \[\leadsto \sin \left({\left(\sqrt{\color{blue}{\sqrt{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt{\tan^{-1}_* \frac{b}{b}}}}\right)}^{\left(b - a\right)}\right)\]

4. Applied sqrt-prod 0.1

   \[\leadsto \sin \left({\color{blue}{\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}} \cdot \sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}}^{\left(b - a\right)}\right)\]

5. Applied unpow-prod-down 0.1

   \[\leadsto \sin \color{blue}{\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)}\]

6. Taylor expanded around -inf 0.1

   \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot \color{blue}{e^{\log \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\frac{1}{4}}\right) \cdot \left(b - a\right)}}\right)\]

7. Simplified 0.1

   \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot \color{blue}{e^{\frac{\log \left(\tan^{-1}_* \frac{b}{b}\right)}{\frac{4}{b - a}}}}\right)\]
8. Using strategy rm

9. Applied add-cube-cbrt 0.1

   \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot e^{\frac{\color{blue}{\left(\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)} \cdot \sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}\right) \cdot \sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}}}{\frac{4}{b - a}}}\right)\]

10. Final simplification 0.1

    \[\leadsto \sin \left(e^{\frac{\left(\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)} \cdot \sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}\right) \cdot \sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}}{\frac{4}{b - a}}} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]

Reproduce

herbie shell --seed 2019151 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))